Under the conditional variational autoencoder (CVAE) [1]} paradigm, we define the CVAE encoder \(q(u | z, z^{\prime })\)  to infer the latent code \(u\) . The ELBO [2]} of this objective can be written as:
\(\mathbb {E}_{z \sim \phi , u \sim q}\left[ D_{KL}{ m(z^{\prime } | z, u) }{ \phi (z^{\prime } | s^{\prime }) } \right] - \beta \mathbb {E}_{z, z^{\prime } \sim \phi } \left[ D_{KL}{ q(u| z, z^{\prime }) }{ p(u)} \right]\) 
